Suggested Citation:"2 How Do Complex Phenomena Emerge from Simple Ingredients?." National Research Council. 2007. Condensed-Matter and Materials Physics: The Science of the World Around Us. Washington, DC: The National Academies Press. doi: 10.17226/11967.

Suggested Citation:"2 How Do Complex Phenomena Emerge from Simple Ingredients?." National Research Council. 2007. Condensed-Matter and Materials Physics: The Science of the World Around Us. Washington, DC: The National Academies Press. doi: 10.17226/11967.

Suggested Citation:"2 How Do Complex Phenomena Emerge from Simple Ingredients?." National Research Council. 2007. Condensed-Matter and Materials Physics: The Science of the World Around Us. Washington, DC: The National Academies Press. doi: 10.17226/11967.

Suggested Citation:"2 How Do Complex Phenomena Emerge from Simple Ingredients?." National Research Council. 2007. Condensed-Matter and Materials Physics: The Science of the World Around Us. Washington, DC: The National Academies Press. doi: 10.17226/11967.

Suggested Citation:"2 How Do Complex Phenomena Emerge from Simple Ingredients?." National Research Council. 2007. Condensed-Matter and Materials Physics: The Science of the World Around Us. Washington, DC: The National Academies Press. doi: 10.17226/11967.

Suggested Citation:"2 How Do Complex Phenomena Emerge from Simple Ingredients?." National Research Council. 2007. Condensed-Matter and Materials Physics: The Science of the World Around Us. Washington, DC: The National Academies Press. doi: 10.17226/11967.

Suggested Citation:"2 How Do Complex Phenomena Emerge from Simple Ingredients?." National Research Council. 2007. Condensed-Matter and Materials Physics: The Science of the World Around Us. Washington, DC: The National Academies Press. doi: 10.17226/11967.

Suggested Citation:"2 How Do Complex Phenomena Emerge from Simple Ingredients?." National Research Council. 2007. Condensed-Matter and Materials Physics: The Science of the World Around Us. Washington, DC: The National Academies Press. doi: 10.17226/11967.

Suggested Citation:"2 How Do Complex Phenomena Emerge from Simple Ingredients?." National Research Council. 2007. Condensed-Matter and Materials Physics: The Science of the World Around Us. Washington, DC: The National Academies Press. doi: 10.17226/11967.

Suggested Citation:"2 How Do Complex Phenomena Emerge from Simple Ingredients?." National Research Council. 2007. Condensed-Matter and Materials Physics: The Science of the World Around Us. Washington, DC: The National Academies Press. doi: 10.17226/11967.

Suggested Citation:"2 How Do Complex Phenomena Emerge from Simple Ingredients?." National Research Council. 2007. Condensed-Matter and Materials Physics: The Science of the World Around Us. Washington, DC: The National Academies Press. doi: 10.17226/11967.

Suggested Citation:"2 How Do Complex Phenomena Emerge from Simple Ingredients?." National Research Council. 2007. Condensed-Matter and Materials Physics: The Science of the World Around Us. Washington, DC: The National Academies Press. doi: 10.17226/11967.

Suggested Citation:"2 How Do Complex Phenomena Emerge from Simple Ingredients?." National Research Council. 2007. Condensed-Matter and Materials Physics: The Science of the World Around Us. Washington, DC: The National Academies Press. doi: 10.17226/11967.

Suggested Citation:"2 How Do Complex Phenomena Emerge from Simple Ingredients?." National Research Council. 2007. Condensed-Matter and Materials Physics: The Science of the World Around Us. Washington, DC: The National Academies Press. doi: 10.17226/11967.

Suggested Citation:"2 How Do Complex Phenomena Emerge from Simple Ingredients?." National Research Council. 2007. Condensed-Matter and Materials Physics: The Science of the World Around Us. Washington, DC: The National Academies Press. doi: 10.17226/11967.

Suggested Citation:"2 How Do Complex Phenomena Emerge from Simple Ingredients?." National Research Council. 2007. Condensed-Matter and Materials Physics: The Science of the World Around Us. Washington, DC: The National Academies Press. doi: 10.17226/11967.

Suggested Citation:"2 How Do Complex Phenomena Emerge from Simple Ingredients?." National Research Council. 2007. Condensed-Matter and Materials Physics: The Science of the World Around Us. Washington, DC: The National Academies Press. doi: 10.17226/11967.

Suggested Citation:"2 How Do Complex Phenomena Emerge from Simple Ingredients?." National Research Council. 2007. Condensed-Matter and Materials Physics: The Science of the World Around Us. Washington, DC: The National Academies Press. doi: 10.17226/11967.

Suggested Citation:"2 How Do Complex Phenomena Emerge from Simple Ingredients?." National Research Council. 2007. Condensed-Matter and Materials Physics: The Science of the World Around Us. Washington, DC: The National Academies Press. doi: 10.17226/11967.

Suggested Citation:"2 How Do Complex Phenomena Emerge from Simple Ingredients?." National Research Council. 2007. Condensed-Matter and Materials Physics: The Science of the World Around Us. Washington, DC: The National Academies Press. doi: 10.17226/11967.

Suggested Citation:"2 How Do Complex Phenomena Emerge from Simple Ingredients?." National Research Council. 2007. Condensed-Matter and Materials Physics: The Science of the World Around Us. Washington, DC: The National Academies Press. doi: 10.17226/11967.

Suggested Citation:"2 How Do Complex Phenomena Emerge from Simple Ingredients?." National Research Council. 2007. Condensed-Matter and Materials Physics: The Science of the World Around Us. Washington, DC: The National Academies Press. doi: 10.17226/11967.

Suggested Citation:"2 How Do Complex Phenomena Emerge from Simple Ingredients?." National Research Council. 2007. Condensed-Matter and Materials Physics: The Science of the World Around Us. Washington, DC: The National Academies Press. doi: 10.17226/11967.

Below is the uncorrected machine-read text of this chapter, intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text of each book. Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.

2
How Do Complex
Phenomena Emerge from
Simple Ingredients?
Most materials are made of simple, well-understood constituents, and yet the ag-
gregate behaviors of materials are stunningly diverse and often deeply mysteriousâa
direct result of the complexity of large systems. Just as a crowd can act in ways un-
characteristic of any individual within it, surprising emergent phenomena are also
seen in collections of electrons, molecules, and even familiar objects such as grains
of sand. For example, sand can be poured like water from a bucket, but unlike any
liquid, it also supports the weight of a person walking on the beach. In the fractional
quantum Hall state, a bizarre liquid state of electrons, an added electron will break
up into new particles, each of which carries a precise fraction of the charge of the
original electron. In a superconductor, an electrical current can flow indefinitely
without decaying. These are impossible feats for individual grains of sand or indi-
vidual electrons. The relationship between the properties of the individual and the
behavior of the whole is very subtle and difficult to uncover and lies at the heart of
condensed-matter and materials physics (CMMP). The challenge is to understand
how collective phenomena emerge, to discover new ones, and to determine which
microscopic details are unimportant and which are essential.
Emergent Phenomena: Beautiful and Useful
Twentieth-century physicists created a spectacularly successful understanding
of the structure of atoms and molecules, the interaction of subatomic particles
with light, and a unified description of all fundamental forces in nature but gravity.
Quantum mechanics and quantum electrodynamics, the most successful quantita-
30

How Do Complex Phenomena Emerge from Simple Ingredients? 31
tive theories developed by humankind, allow for extraordinarily accurate calcula-
tions of the properties of individual and small collections of particles.
Nature, however, confronts us with materials consisting of unimaginably large
numbers of particles. For example, there are many more electrons in a copper
penny than there are stars in the known universe. It is therefore not surprising that
condensed-matter and materials physicists regularly discover phenomena that nei-
ther were foreseen nor are easily understood. These phenomena emerge as collective
aspects of the material at hand. Emergent phenomena are properties of a system of
many interacting parts that are not properties of the individual microscopic con-
stituents. It is often not readily possible to understand such collective properties
in terms of the motion of individual constituent particles. Emergent phenomena
occur at all scales, from the microscopic to the everyday to the astronomical, and
from the precincts of quantum mechanics to the world known to Newton and
Maxwell. The infinite diversity of emergent phenomena ensures that the beauty,
excitement, and deep practical utility of condensed-matter and materials physics
comprise an inexhaustible resource.
Emergent phenomena are not merely academic curiosities. Some, like the
emergence of life from biomolecules, define our very existence. Others, like the
regular arrangements of atoms in crystals, are simply so familiar that we rarely
even pause to wonder at them anymore. There are countless examples of this kind.
At the same time, the discovery and study of emergent phenomena often lead to
immensely important practical applications. Superconductivity, discovered almost
100 years ago, is a good example. While Dutch physicist Kamerlingh Onnes did
envision producing magnetic fields using solenoids wound from superconduct-
ing wire, he could never have foreseen superconducting magnets big enough to
surround a human, nor that such a magnet would be the heart of a technological
marvel (magnetic resonance imaging; see Figure 1.1 in Chapter 1) that would
revolutionize medicine. Looking ahead, one can imagine that the recently discov-
ered high-temperature superconductors, which have so far seen limited applica-
tion, might ultimately play a major role in reducing world energy consumption
by allowing lossless transmission of electrical power over long distances. Unlike
superconductors, which took many decades to see large-scale application, there is
the very recent dramatic example of giant magnetoresistive materials, which came
to dominate hard disk data storage in just a few years. Liquid crystalline materials,
in which large numbers of asymmetric molecules in solution exhibit a dizzying
variety of emergent phases, are used in everyday electronics like cellular telephones
and laptop computers. Jamming of granular materials (discussed below), perhaps
unfamiliar to the average citizen, is an emergent phenomenon with real economic
consequences in the mining, pharmaceutical, and other industries. And the list
goes on.
Emergent phenomena are so widespread that a comprehensive review is both

32 C o n d e n s e d - M at t e r and M at e r i a l s P h ys i c s
impossible and inappropriate. The Committee on CMMP 2010 fully expects that
much of the most significant research in the coming decade, as was true of past
decades, will be triggered by the discovery of new emergent phenomena that are
unlikely to be anticipated in any present list of âmost importantâ problems. Here, a
few examples are discussed to illustrate the quest, which underlies much of CMMP,
to understand the relation between the properties of the âmicroscopicâ constituents
of matter and the macroscopic behavior of the whole.
Superconductivity, a century-old phenomenon, is discussed first because it is
both an extraordinarily dramatic example of emergence and one of the most ac-
tive fields of research in CMMP today. That example is followed by more general
discussions of current trends in research on Fermi and non-Fermi liquids, on
quantum Hall effect systems, and on critical phenomena and universality in clas-
sical and quantum-phase transitions. Emergence in ultracold atomic gases and in
granular matter round out the list of case studies. (Further discussion of important
emergent phenomena in CMMP can be found elsewhere in this report, especially
in Chapter 4 on the physics of life and Chapter 5 on systems far from equilibrium.)
Following the examples are some brief remarks on how to realize the full potential
of emergence.
Superconductivity: An Illustrative
Example and a Frontier of Research
In many materials, exotic and unexpected phenomena emerge from strong
interactions between the constituent particles at the microscopic level. Quantum
mechanics often plays a key role and renders the phenomena particularly puzzling
and counterintuitive. Superconductivity, the property of certain materials to carry
electrical currents without any dissipation of energy, is the quintessential example
of such a quantum emergent phenomenon. First discovered in mercury in 1911 by
Kamerlingh Onnes and his graduate student Holst in their pioneering experiments
on the properties of matter near the absolute zero of temperature, superconductiv-
ity was utterly unheralded and resisted explanation for nearly 50 years. Nowadays,
CMMP researchers have a good understanding of the phenomenon in mercury and
other similar metals where the transition to the superconducting state occurs at
very low temperature. But nature is much more resourceful, and this comfortable
situation was radically upset just 20 years ago with the discovery of a new class of
superconductors having much higher transition temperatures. No accepted theory
of high-temperature superconductivity has yet been developed, in spite of immense
effort and the application of the most sophisticated tools of theoretical physics by
large numbers of researchers across the globe. Unlike the low-temperature metallic
superconductors, these new materials are not completely understood even in their
normal, non-superconducting, states. Indeed, high-temperature superconductors

How Do Complex Phenomena Emerge from Simple Ingredients? 33
highlight one of the broadest and most important current problems in all physics,
the strongly interacting quantum many-body problem.
All materials conduct electric current to some extent, but the amount of force
that must be applied to maintain a current varies greatly from material to material.
The resistance of a material quantifies how large a voltage must be applied to ob-
tain a given amount of current flow. Put another way, to maintain a given amount
of current consumes power in proportion to the resistance. In a superconductor,
the resistance is precisely zero, so a persistent current can flow, forever, around a
superconducting ring without need of a battery or a generator!
In an attempt to be quantitative about the meaning of âforever,â measurements
have been carried out to try to detect the rate of decay of persistent currents in
superconducting rings. In these experiments, the current in a ring is measured very
accurately at an initial time and then again a long time later. Despite the extreme
accuracy of these measurements, no decrease in the current is detected. Even if the
current were decaying at the fastest rate possible consistent with the accuracy of the
measurement, the current would not decay within the age of the universe.
Superconductivity appears when the temperature is reduced below a critical
value. What this means is that the resistance of a metal, such as the mercury stud-
ied by Kamerlingh Onnes, has a non-zero value at a temperature just a fraction
of a degree above the critical temperature. However, at any temperature below
the critical temperature, the resistance is zero. It is the same piece of metal both
above and below the critical temperature, and the same electrons are carrying the
current. At the critical temperature, something subtle but spectacular happens in
the organization of the vast number of electrons in the metal that causes them to
form a superconducting state.
Normally, scientists think of quantum mechanics as the set of physical prin-
ciples that govern the motion of small numbers of microscopic particlesâatoms
and electrons and nuclear matter. Quantum mechanics is usually only indirectly
seen in the properties of macroscopic matterâobjects large enough to hold in
oneâs hand. However, superconductors have many counterintuitive properties that
reflect their underlying quantum nature. The existence of a persistent current is a
concrete demonstration of quantum mechanics at a macroscopic scale. Since cur-
rents produce magnetic fields, it is perhaps not surprising that the magnetic prop-
erties of superconductors are likewise unprecedented. Indeed, in 1933 Meissner
and Oschenfeld discovered that superconductors entirely expel (small) magnetic
fields from their interior. In fact, in a superconducting quantum interference device
(SQUID), a relation exists between the frequency of current oscillations and an
applied voltage that only involves the charge of the electron and the fundamental
constant of quantum mechanics, Planckâs constant. This relation has been found
experimentally to be universal to a precision of better than 3 parts in 1019, which
means that clocks based on two independent Josephson junctions kept at the same

34 C o n d e n s e d - M at t e r and M at e r i a l s P h ys i c s
voltage would differ from each other by no more than one-tenth of a second over
a time interval equal to the age of the universe! It is inconceivable that any of the
founders of quantum mechanics could have foreseen that a measurement of mac-
roscopic quantities would depend directly, and with such precision, on the laws of
quantum mechanics. Finally, macroscopic quantum phenomena are certainly not
limited to superconductors. The ordinary magnet holding up a note on a kitchen
refrigerator offers a dramatic everyday example: A steady magnetic field is present
without any battery to keep currents flowing. This macroscopic quantum phenom-
enon is just as spectacular as the persistent currents in a superconductor.
One of the great triumphs of 20th-century CMMP is the microscopic theory of
superconductivity in ordinary metals, the Bardeen-Cooper-Schrieffer (BCS) theory.
Not surprisingly, since superconductivity involves only a subtle, low-Â­temperature
change in the properties of the electrons in the metal, the BCS theory is based on the
equally successful Fermi liquid theory of the properties of normal metals. (Fermi
liquid theory and its breakdown are discussed below.) Moreover, hundreds of dif-
ferent metals that are BCS superconductors have been identified, although mostly
with superconducting transition temperatures less than 10 K. While the theory has
rarely led to the prediction of new superconductors, it has provided qualitative
guidance for the search for new, low-temperature superconductors.
Starting with the 1986 discovery of superconductivity at 30 K in La2âxBaxCuO4
by Bednorz and Mueller, a new class of materials, now known as high-temperature
superconductors, became the focus of intensive research. The highest supercon-
ducting transition temperature found to date in these materials is approximately
150 K in HgBa2Ca2Cu3O8+x under pressureâroughly 10 times higher than any
previously known superconductor. The microscopic interactions responsible for
the transition to the superconducting state are different from those in BCS super-
conductors. Moreover, the so-called normal state observed at temperatures above
the superconducting transition is very different from that of a normal metal and
is not well understood.
The high-temperature superconductors belong to a large class of synthetic
materials (i.e., they do not appear in nature) known as highly correlated electronic
materials (see Figure 2.1). Research in this area in the past two decades has been
rich in discovery and in producing challenges to the entire quantum theory of
solids. These new materials exhibit a startling array of emergent phenomena: fer-
romagnetism and antiferromagnetism, orbital ordering and long-period charge
ordering, giant and colossal magnetoresistance, new types of superconductivity
with new forms of broken symmetry, and all sorts of fluctuation phenomena over
unprecedentedly wide ranges of temperature and material parameters. Obtaining
a well-founded qualitative understanding of the normal state, at the level of the
Fermi liquid theory of simple metals, is among the most challenging and most
profound problems facing CMMP. Clearly, understanding the mechanism of high-

How Do Complex Phenomena Emerge from Simple Ingredients? 35
FIGURE 2.1â Local electronic structure of a highly correlated electronic solid visualized with sub-
atomic-scale resolution using a scanning tunneling microscope. This is not an Abstract Impressionist
painting. It is a self-organized structure âseenâ on the smooth, cleaved surface of a crystal of the
high-temperature superconductor Bi2Sr2CaCu2O8+Î´. The patterns represent changes in the electronic
structure that are pinned in a highly organized but ultimately random (âglassyâ) pattern. The detailed
information concerning the organized structures of electrons in solids that this kind of experiment
provides has opened unprecedented opportunities to explore the ultimate connections between micro-
scopic physics and the emergent properties of materials. SOURCE: Y. Kohsaka, C. Taylor, K. Fujita, A.
Schmidt, C. Lupien, T. Hanaguri, M. Azuma, M. Takano, H. Eisaki, H. Takagi, S. Uchida, and J.C. Davis,
âAn Intrinsic Bond-Centered Electronic Glass with Unidirectional Domains in Underdoped Cuprates,â
Science 315, 1380-1385 (2007). Reprinted with permission from the American Association for the
Advancement of Science.
temperature superconductivity at a level that can provide qualitative guidance for
the search for other, possibly even higher-temperature superconductors is a prob-
lem of enormous importance. It is surely not an accident that so many other sorts
of emergent states (ordered phases) occur in this class of materialsâunderstanding
the relation between the various types of ordered phases of these materials and
understanding how they relate to the properties of the non-Fermi liquid normal

36 C o n d e n s e d - M at t e r and M at e r i a l s P h ys i c s
phase are problems that will occupy much of the focus of CMMP in the coming
decade.
Fermi Liquids and Non-Fermi Liquids
If one could ignore the interactions between electrons in a solid, the proper-
ties of the material could be derived from a theory that treats only one electron
at a time. While this might seem to be an absurd assumption, since electrons are
charged and repel one another strongly, such single-electron theories often work
remarkably well. Quantum mechanics is essential for understanding why this is
so. All electrons are intrinsically identical to one another, just as are all protons,
all neutrons, and so forth. Quantum mechanics sets very stringent rules for the
behavior of systems containing many identical particles. If the positions of two
identical particles are interchanged, quantum mechanics naturally insists that there
be no observable consequence. Except in certain rare cases to be described below,
there are only two ways in which the quantum wave function of the material can
satisfy this requirement: either (1) nothing at all happens to the wave function
upon interchange of two particles, or (2) it changes its sign. Particles for which the
wave function changes sign are called fermions, while those for which the sign is
preserved upon interchange are known as bosons.
Electrons are fermions, and thus a many-electron wave function changes sign
when two are interchanged. This property underlies the Pauli exclusion principle,
which high school chemistry students are usually told means that no two electrons
can be in the same place at the same time. More precisely, two electrons are forbid-
den from occupying the same quantum state. Despite their vagueness, these state-
ments make it easy to see why the Pauli principle has such vast significance for the
theory of materials. If no two electrons can be in the same place at the same time,
they rarely get so close together that their mutual repulsion is extremely strong. If
no two can occupy the same quantum state, then at low temperatures the many
electrons in a material are forced to sequentially occupy higher and higher energy
levels, forming a âFermi sea.â In some circumstances, interactions between electrons
are not strong enough to disturb any but the relatively few levels that are near the
surface of this sea. In effect, the Pauli principle converts what at first appears to be
a hopelessly strongly interacting system into a more weakly interacting one. In a
nutshell, this is why scientists understand the properties of simple metals as well
as they do.
Remarkably, a more sophisticated version of the âFermi liquidâ picture just
described often works very well even when the repulsive interactions between
electrons are fairly strong (compared to the average kinetic energy of electrons).
In these cases, the properties of the material can be described in terms of new enti-
ties, known as quasi-particles, which behave in much the same way as the original

How Do Complex Phenomena Emerge from Simple Ingredients? 37
particlesâthat is, electronsâexcept that they do not interact strongly with one
another (see Figure 2.2). One can think of these quasi-particles as consisting of an
electron plus a disturbance among the other electrons around it. In some cases,
the quasi-particles behave so similarly to the original electrons that it is hard to
remember that they are distinct objects. In other cases, the quasi-particle behaves
like an electron with strongly modified propertiesâfor instance, in the âheavy
fermion materials,â metal alloys containing heavy elements such as uranium and
cerium, the quasi-particle can be as much as a thousand times heavier than an
electron. A system in which the properties of a dense electron fluid can be related
to those of a gas of weakly interacting quasi-particles is called a Fermi liquid. The
very successful theory of normal metals, as well as the equally successful theory of
simple semiconductors, is based on Fermi liquid theory.
However, in many electronically interesting solids, over a wide range of tem-
peratures, pressures, and compositions, the Fermi liquid description fails badly.
This class includes many of the most interesting materials that have been Â­discovered
a b
4 *1/3
Amplitude (nâ¦cm)
2
0.2 0.4 0.6 0.8 1.0 1.2
Temperature (K)
0
2
0.07 0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.15
1 / B (T 1 )
FIGURE 2.2â Signatures of the Fermi liquid state in Sr2RhO4, a strongly correlated material. (Left) A
map of the Fermi surface (constant energy surface at the Fermi level) in reciprocal space revealed by
high-resolution angle-resolved photoemission experiments. (Right) The resistance as a function of
magnetic field at temperatures close to absolute zero; these âquantum oscillationsâ reflect the shape of
the Fermi surface. Despite the fact that this material is structurally extremely similar to cuprate high-
2-2 a, b
temperature superconductors (such as La2CuO4+Î´), these experiments unambiguously demonstrate
that at low-enough energies, the electronic properties of Sr2RhO4 are perfectly represented by a gas
of essentially non-interacting, electron-like âquasi-particles.â SOURCE: Reprinted with permission
from F. Baumberger, N.J.C. Ingle, W. Meevasana, K.M. Shen, D.H. Lu, R.S. Perry, A.P. Mackenzie, Z.
Hussain, D.J. Singh, and Z.-X. Shen, âFermi Surface and Quasiparticle Excitations of Sr 2RhO4,â Phys.
Rev. Lett. 96, 246402 (2006). Copyright 2006 by the American Physical Society.

38 C o n d e n s e d - M at t e r and M at e r i a l s P h ys i c s
and studied in the past two decades, among them the high-temperature super-
conductors and quantum Hall effect systems. There are many well-understood
qualitative reasons why Fermi liquid theory is less successful in these new materials.
More importantly, the experimental evidence that the behavior of these systems is
incompatible with Fermi liquid theory is clear and incontrovertible. This evidence
ranges from direct tests of the quasi-particle hypothesis, such as angle-resolved
photoemission measurements that can directly âseeâ a quasi-particle if it exists, to
indirect tests, such as a measured metallic resistivity that exceeds the maximum
that is consistent with the quantum motion of independent quasi-particles. Lack-
ing today is a conceptually clear and computationally tractable framework for
understanding the properties of a ânon-Fermi liquidâ of electrons.
Some of the essential ingredients in an understanding of a non-Fermi liquid
are clear. The basic objects that move are no longer electrons, but more likely
large clusters of electrons moving in concert. The building blocks of a theory of
such a state are thus very different from the quasi-particles of Fermi liquid theory.
A better intuitive picture may come from envisaging a fluid made up of pieces
of melted electron crystals, or magnets, or superconductors, not just individual
quasi-particles. Correspondingly, the properties of such a system are not readily
inferred from the properties of individual electrons. For instance, a fluid of par-
tially ordered magnets can have magnetic properties intermediate between those
of a magnet and a normal metal (see Figure 2.3). Such behavior is most readily
addressed in the proximity of a âquantum critical pointâ separating two distinct
phases, as discussed below.
However, this is just the tip of the iceberg. The broad occurrence of non-Fermi
liquid phenomena suggests that it is related to new quantum phases, or at least to
extremely new regimes of matter. Correlated motion of many particles is difficult
to characterize and still more difficult to understand. However, the non-Fermi
liquid character exhibited by a rapidly increasing number of interesting materials
imbues the problem with an immediacy and focus that is compelling. Moreover,
various new theoretical ideas, new experimental discoveries, and methodological
advances in theory and experiment (some of which are discussed in Chapter 11)
give hope that substantial advances in understanding are occurring.
One set of new ideas involves the existence of broken-symmetry quantum
phases possessing âhiddenâ (i.e., hard to detect) types of order. For example, interest
has recently focused on a class of states with complex patterns of spontaneously
generated persistent currents. No such state has yet been unambiguously identified
in a real material; conversely, even if such a state occurs, it would be very difficult
to detect by most conventional measurements.
Another interesting class of states with hidden order is electronic analogues
of the classical liquid crystalline states that occur in complex fluids. In a simple
liquid, the particles can flow from one point to another, all points in space are

How Do Complex Phenomena Emerge from Simple Ingredients? 39
a b
FIGURE 2.3â Calculated magnetic structure factor for a âstripe-orderedâ antiferromagnet. Strong
interactions between electrons can lead to complex ordered states with particle-like excitations that
look nothing like those of an electron. One such state, which has been directly identified in neutron
2-3 a, b
scattering experiments on a number of transition metal oxides, including some high-temperature su-
perconductors (such as La2CuO4+Î´), is a unidirectional incommensurate antiferromagnet, or âstriped
phase,â shown schematically (right panel). The emergent particle-like excitations that occur in such
a state are charge-neutral âspin-waves,â whose spectrum is calculated here (left panels) and which
are valid deep in the ordered phase. SOURCE: (Left) Reprinted with permission from D.X. Yao, E.W.
Carlson, and D.K. Campbell, âMagnetic Excitations of Stripes and Checkerboards in the Cuprates,â
Phys. Rev. B 73, 224525 (2006). Copyright 2006 by the American Physical Society. (Right) Steven A.
Kivelson, Stanford University.
equivalent, and all directions are the same. In a crystal, there is a lattice on which
the atoms or molecules are localized in a pattern that repeats periodically through
space, so that different points within the unit cell are different from each other,
and different directions, relative to the axes of symmetry defined by the crystal-
line order, are distinct from each other. Liquid crystalline states exhibit patterns of
symmetry breaking intermediate between those of a simple liquid and a crystal.

40 C o n d e n s e d - M at t e r and M at e r i a l s P h ys i c s
For instance, a ânematicâ is a uniform fluid state in which one spatial direction is
distinguished from the other two. Traditionally, a nematic is described as consist-
ing of a fluid of cigar-shaped molecules, in which the molecules can flow, but they
are preferentially oriented along one direction. At first sight, a nematic electron
fluid seems improbable, since electrons are point-like, not cigar-shaped. However,
in some circumstances it is legitimate to think of a highly correlated electron
fluid as consisting of melted fragments of an appropriate electron crystal; these
fragments, in turn, can play the role of the cigar-shaped molecules in the classical
nematic. An electron nematic phase is also difficult to detect for various technical
reasons, including the fact that crystalline imperfections can mask its occurrence
on Â­macroscopic scales and that it can be hard to distinguish from a more conven-
tional strain-driven change in the crystal structure of the host material. However, as
discussed below, strong evidence for an electronic nematic phase has recently been
found in extremely high mobility quantum Hall devices. Moreover, evidence of the
existence of such phases has recently been found in a number of interesting highly
correlated materials, including Sr3Ru2O7 and certain of the high-Â­temperature superÂ­
conductors (e.g., La2âxBaxCuO4).
A still more revolutionary circle of ideas, built around the notion of âfractional-
izedâ phases, has been the focus of increasing attention in recent years. The key idea
here is that sharp distinctions can exist between distinct quantum phases of matter
that have nothing to do with distinct patterns of symmetry breaking. Rather, these
phases are characterized by an abstract form of orderâso-called topological order.
Because the order is so subtle, it is difficult to establish experimentally where such
phases occur in nature. The most directly experimentally accessible characteristic
of these phases is the existence of new types of quasi-particles that behave like a
âfractionâ of an electron. For instance, in one of the best theoretically characterized
of these phases, there are no quasi-particles that carry both the charge and spin of
ordinary electrons. Instead, two new and very strange kinds of particles appear, one
of which carries only spin and another of which carries only charge. In other sys-
tems, the quasi-particles carry a specific fractionâfor example, one-thirdâof the
electron charge. Under some circumstances, these quasi-particles are also believed
to possess âfractionalâ quantum statistics. In other words, the wave function of two
such identical particles neither preserves nor changes its sign when the particles are
interchanged but instead is multiplied by a complex number (e.g., the cube root
of â1!). Such particles are neither bosons nor fermions; they are called anyons.
At present, fractionalization is an established experimental fact only in the
fractional quantum Hall state, as explained in the next section. Evidence suggestive
of the existence of fractionalized phases has been reported in the past few years in
a number of strongly correlated materials that exhibit particularly unusual proper-
ties. Moreover, the search for fractionalized states has gained added impetus from
the realization, discussed in Chapter 7, that such phases might produce uniquely

How Do Complex Phenomena Emerge from Simple Ingredients? 41
favorable structures for the construction of a quantum computer. However, it is
an issue for the coming decade to discover which of these phases actually exist in
nature, and where (i.e., in what materials).
Quantum Hall Systems and the Discovery
of New Quantum States of Matter
The concepts of fractionalization and non-Fermi liquids have roots in elec-
tronic materials that are less than three-dimensional. For example, it has been
known since the 1960s that a disorder-free, one-dimensional electron system can-
not be a Fermi liquid. Unlike electrons in two and three dimensions, the distribu-
tion in momentum space of one-dimensional electrons does not have a discontinu-
ity at the Fermi momentum, even at zero temperature. Experimental evidence for
such âLuttingerâ liquids has accumulated in recent years from studies of electrical
conduction in carbon nanotubes and along the edges of two-dimensional electron
systems in a high magnetic field, as well as from more complex experiments (such
as angle-resolved photoemission and optical conductivity) performed on various
other âquasi-one-dimensionalâ materials in which electrons can move readily only
in one direction.
Fractionalization is already well known in two-dimensional electron systems
(see Figure 2.4). A large magnetic field perpendicular to the two-dimensional plane
breaks up the otherwise-continuous distribution of electron energies into a ladder
of discrete states known as Landau levels. Since the energy of an electron in a cir-
cular cyclotron orbit does not depend on where the orbit is located, each Landau
level can hold many electrons, the total number being proportional to the mag-
netic field. Consequently, at sufficiently high magnetic fields, all two-dimensional
electrons in a given sample can fit into the lowest Landau level and have precisely
the same kinetic energy. With no variation in the kinetic energy, the Coulomb
interaction between electrons completely dominates the physics in clean samples.
In a real sense this is the most strongly interacting quantum system imaginable. It
is in this regime that Tsui, Stormer, and Gossard discovered the famous fractional
quantum Hall effect (FQHE) in 1982. They observed that when the lowest Landau
level is one-third filled, a wholly unexpected quantized plateau in the Hall resis-
tance appears, signaling the opening of an energy gap. Shortly thereafter, Laughlin
explained the effect as the emergence of a new state of matter, one driven entirely
by strong Coulomb correlations among the electrons. Laughlinâs theory was the
âD.C. Tsui, H.L. Stormer, and A.C. Gossard, âTwo-Dimensional Magnetotransport in the Extreme
Quantum Limit,â Phys. Rev. Lett. 48, 1559 (1982).
âR.B. Laughlin, âAnomalous Quantum Hall Effect: An Incompressible Quantum Fluid with Frac-
tionally Charged Excitations,â Phys. Rev. Lett. 50, 1395 (1983).

42 C o n d e n s e d - M at t e r and M at e r i a l s P h ys i c s
FIGURE 2.4â Quantum phases and phase transitions in a two-subband quantum Hall device. Shown
here is a contour map of the resistivity of a two-dimensional electron gas that has been trapped at
the interface between two semiconductors. The y-axis is the gate voltage applied across the sample
(which changes the density of electrons), and the x-axis is the strength of an applied magnetic field.
The dark regions, where the resistivity becomes vanishingly small as the temperature tends toward
absolute zero, are various quantum Hall effect states, where the integers label the value of the quan-
tized Hall conductance in units of the quantum of conductance. The bright regions mark the points
at which quantum phase transitions occur between the different phases. The fact that the resistance
neither vanishes nor diverges as the temperature tends to zero along the quantum critical lines is a
tangible reflection of the existence of quantum fluctuations at all length scales. SOURCE: Reprinted
with permission from X.C. Zhang, D.R. Faulhaber, and H.W. Jiang, âMultiple Phases with the Same
Quantized Hall Conductance in a Two-Subband System,â Phys. Rev. Lett. 95, 216801 (2005). Copyright
2005 by the American Physical Society.
first to imply the existence of fractionalized elementary particles within a strongly
correlated electron system. These new particles, which carry precisely one-third the
charge of an ordinary electron, are neither bosons nor fermions, possessing instead
the bizarre anyonic exchange statistics mentioned above. Very strong experimental
evidence for the fractional charge of these particles now exists, and experimental
proof of fractional statistics is currently being hotly pursued.
The FQHE at one-third filling of the lowest Landau level turned out to be only
one member of a large family of similar correlated phases of two-dimensional elec-

How Do Complex Phenomena Emerge from Simple Ingredients? 43
trons. Over the past 25 years, many dramatic experimental observations have been
made, and a sophisticated and unified theoretical understanding of much of FQHE
phenomenology has been developed. The field remains vibrant, with the pace of
new discoveries paralleling the steadily increasing quality of the semiconductor het-
erostructure samples grown by molecular beam epitaxy. Most recently, interest has
focused on an FQHE that appears at one-half filling of the first excited Landau level
(the so-called 5/2-state). This fragile state is expected to possess an even stranger
form of exchange statistics in which the outcome of multiple interchanges of pairs
of particles depends on the order in which the interchanges occur. Observation of
such ânon-Abelianâ statistics would have deep fundamental significance for phys-
ics and possible impact on schemes for quantum computation, since non-Abelian
systems are anticipated to be especially insensitive to the kinds of disturbances that
ordinarily disrupt quantum coherence.
The steady increase in sample quality has also led to the recent discovery of new
electronic phases outside the FQHE paradigm. At modest magnetic fields, where
several Landau levels are occupied, collective states emerge that are reminiscent
of both classical liquid crystals and pinned charge density waves. For example,
near one-half filling of highly excited Landau levels, electrical conduction in the
two-dimensional system spontaneously becomes extremely anisotropic at very
low temperature (below about 150 mK). Strikingly, this anisotropy disappears on
moving slightly away from one-half filling and is absent altogether at both very
low and very high magnetic fields. The effect is widely believed to reflect a stripe-
like pattern of charge density modulation in the two-dimensional system. While
quantum and thermal fluctuations destroy the long-range order of the stripes,
local order persists. In effect, the two-dimensional electron system is broken up
into a collection of striped domains. Above about 150 mK, these domains are ap-
parently randomly oriented, and the net resistivity of the system is isotropic. At
lower temperatures, orientational order sets in and the resistivity rapidly becomes
anisotropic. As discussed above, this situation is highly analogous to the isotropic-
to-nematic phase transition in classical liquid crystals (see Figure 2.5). In this case,
the local stripe domains of electrons play the role of the funny-shaped molecules
in the liquid crystal. That a system of point-like electrons would emulate a liquid
crystal is one of the most dramatic examples of emergence in recent years.
Excitingly, the quantum Hall effect has recently been observed in graphene
(single atomic layers of graphite). This is especially interesting since graphene is
a semimetal whose low-energy band structure precisely mimics the dynamics of
massless relativistic particles, the so-called Dirac fermions familiar to high-energy
physicists. In other words, the kinetic energy of electrons (or holes) in graphene
is directly proportional to their momentum, rather than its square. This aspect
(and others) of the graphene band structure creates a spectrum of quantum Hall
states that is distinct from that found in conventional two-dimensional electronic

44 C o n d e n s e d - M at t e r and M at e r i a l s P h ys i c s
FIGURE 2.5â Quantum and classical nematic liquid crystals. The background image is a polarization
microscope image of a classical nematic liquid crystal, similar to those found in cellular telephones,
computer displays, or wristwatches. The graph and the insets describe the development of quantum
liquid crystalline behavior in a collection of electrons moving on a plane surface of a nematic liquid
crystal in the presence of a perpendicular magnetic field. The red and blue traces show how the electri-
cal resistance of the system, measured in two mutually perpendicular directions, becomes extremely
anisotropic at temperatures close to absolute zero. This anisotropy is believed to arise from the spon-
taneous orientational ordering of small elongated clumps of electrons, as suggested by the black rods
in the lower insets. SOURCES: (Graph) J.P. Eisenstein, âTwo-Dimensional Electrons in Excited Landau
Levels: Evidence for New Collective States,â Solid State Commun. 117, 123-131 (2001). (Background
image) Photograph by Oleg D. Lavrentovich, Liquid Crystal Institute, Kent State University.
materials (e.g., in silicon inversion layers or gallium arsenide quantum wells).
To date, only integer, as opposed to fractional, quantized Hall states have been
detected in graphene. This suggests that the quality of the current samples is not
high enough for the subtle, many-particle correlations of the FQHE to hold sway

How Do Complex Phenomena Emerge from Simple Ingredients? 45
over the disordering effects of impurities. The intensity of research on graphene is
now enormous. There is every reason to believe that significant advances, including
the discovery of new emergent phenomena and the development of more effective
means for creating, manipulating, and employing clean graphene films, will occur
in the coming decade.
Clearly, the nature of correlated motion of strongly interacting particles is a
conceptually deep problem with broad implications in areas of condensed-matter
and materials physics and in other areas of physics as well. The quest to understand
the emergent behaviors produced by these correlations is one of the central issues
in physics today. Moreover, with the spirit of the past as a prologue, there is every
reason to believe that some of these new emergent phenomena will be the basis of
future technologies of profound importance.
Critical Phenomena and Universality
Generally, the phases of matter are well defined in the sense that many of the
properties of a given material depend primarily on the materialâs state (for example,
solid, liquid, or gas), and not so much on the substance itself. All liquids behave in
many familiar ways; as elementary school students learn, a liquid has a fixed volume
but takes the shape of its container; it flows; sound can propagate through it; and
so forth. These and many other features are common to liquid water, gasoline, al-
cohol, and liquid helium. A metalâbe it copper or silver or an organic metal made
largely of carbon and hydrogenâis shiny and conducts electricity readily. Indeed,
an organic metal and an organic insulator, even though they may be made of es-
sentially the same constituent elements, have physical properties that share many
fewer features than do an organic metal and copper. This universal character of the
phases of matter generally holds all the way from the nanometer to the centimeter
scale and beyond.
Phase transitions can occur as a function of temperature, or pressure, or
magnetic field, or composition, and so forth. When water freezes, the water at
temperatures just below the freezing point is a solid (ice), which behaves pretty
much in the same way as ice that is far colder. The water just above the freezing
point is a liquid, and similar to liquid water at higher temperatures. The change in
the behavior is highly discontinuous across the freezing point. This is an example
of a first-order transition.
Some other transitions, such as the transition from a paramagnetic to a fer-
romagnetic phase, occur in a much more mysterious manner, by a âcontinuous
transition.â Close to the critical temperature, it becomes increasingly difficult
to tell which side of the transition the system is on. On length scales that get
increasingly large in proximity to the transition, the system cannot decide which
phase behavior to exhibit, and so it exhibits a new, intermediate behaviorâcritical

46 C o n d e n s e d - M at t e r and M at e r i a l s P h ys i c s
b
Â­ ehaviorâthat is different from the behavior of either of the phases themselves.
At a critical point, there are fluctuations on all length scales from the microscopic
to the macroscopic.
The broad distribution of length scales at a critical pointâor technically, the
scale invarianceâis a spectacular phenomenon. Most phenomena in nature have
a characteristic size. Atoms are all (within a factor of two) a couple of angstroms
in diameter, and people are typically 5 to 6 feet tall. In a piece of ice, when atoms
rearrange (i.e., flow on a microscopic scale), typically only a few atoms move at a
time. However, near a ferromagnetic critical point, collective motions occur involv-
ing reorientation of the magnetic dipoles of small groups of a few electrons and
enormous patches of millions or billions of electrons.
The ârenormalization groupâ theory of critical phenomena in classical systems
undergoing a continuous phase transition, which was developed throughout the
last three decades of the 20th century, is one of the most significant contributions
of CMMP to science. It provides an understanding of how scale invariance at a
critical point arises from simple microscopic interactions. Because physics near a
critical point occurs on such a broad range of length scales, much of the detailed
information about the microscopic constituents of the material is averaged out. In a
quantifiable sense, the behavior of systems near a critical point is âuniversalââthat
is, precisely the same for different systems. Not only does the magnetization grow
with decreasing temperature in precisely the same way in ferromagnets made of
pure iron or of neodymium alloys, but it grows in exactly the same way that the
concentration difference grows near the critical point for phase separation of a
mixture of water and oil.
Indeed, renormalization group theory offers a top-down perspective for un-
derstanding condensed matter that is opposite to the usual bottom-up reductionist
approach, which focuses on the identification of a small number of elementary
building blocks. Since the behavior of the system is independent of what material
is being studied, there is not a unique route from the microscopic understanding
of the laws of quantum mechanics to the macroscopic properties of a system near
its critical point. Rather, the âanswerâ is largely independent of the âquestion.â So
powerful is the notion of universality that the solution of even a vastly simplified
abstract mathematical model problem, so long as it respects certain symmetries
and constraints of the real world, can be used to obtain a precise and quantitative
understanding of experimental observations in the complex real world! This is the
most precisely understood realization of the more general notion of emergence.
As with any revolutionary change, the full implications of the renormalization
group approach continue to reverberate. When continuous phase transitions occur
at zero temperature, quantum mechanics on a macroscopic scale becomes impor-
tant. Here, quantum mechanics intertwines dynamics and thermodynamics in a
way that they never are in finite temperature (âclassicalâ) phase transitions. The

How Do Complex Phenomena Emerge from Simple Ingredients? 47
naÃ¯ve extension of the successful theory of classical phase transitions has already
been shown to produce results that are in conflict with experiment for quantum
phase transitions. It remains unclear whether minor modifications of the classical
approach or much more fundamental changes are needed to address these difficul-
ties. Transitions occur, as well, in non-equilibrium, âdrivenâ Â­dynamical systems, of
which the best known is the transition from laminar flow to turbulence. Many driven
dynamical systems exhibit phenomena on a broad range of scalesâexhibitingÂ­ an
approximate form of scale invariance. Much beautiful work has already been done
applying renormalization group ideas to this broad class of systems, but it is clearly
just the tip of the iceberg, as discussed in Chapter 5. Â­Another vast area in which
many related open problems exist is systems with quenched disorderâin which
there are degrees of freedom, such as the locations of impurity atoms, which are
not in thermal equilibrium. Phase transitionsâeven classical phase Â­transitionsâin
the presence of quenched disorder are not fully underÂ­stood, and where quenched
disorder and quantum phase transitions intersect, there is a growing understanding
that entirely new conceptual tools are needed.
Emergence in UltraCold Atomic Gases
The rapidly dissolving boundary between conventional atomic physics and
CMMP has focused yet another spotlight on the phenomenon of emergence. The
convergence of these two fields began about 10 years ago when, upon cooling dilute
gases of atoms (e.g., 87Rb) trapped in magnetic bottles into the nano-kelvin tem-
perature range, atomic physicists succeeded in directly witnessing the phenomenon
of Bose-Einstein condensation (BEC). In a BEC, quantum uncertainty obscures
the identity of the individual atoms and instead endows the entire ensemble with
a single coherent wave function. While Bose-Einstein condensation had been long
known to CMMP physicists to be responsible for the phenomenon of superfluidity
in liquid helium, its unambiguous observation in a wide variety of highly control-
lable atomic systems was a watershed event in physics.
Since the initial observations of BEC, the field of ultracold atomic gases has
expanded dynamically in both experiment and theory. Particularly dramatic among
many exciting developments has been the observation of Cooper pairing in cold
fermionic systems and the detection of the superfluid-to-insulator transition
among cold bosonic atoms held in an optical lattice potential. These two examples
illustrate the power of the ultracold atom field to study classic condensed-matter
phenomena in an extremely controllable way. Moreover, ultracold atoms in spe-
cially tailored optical lattices, as described in Chapter 8, may be used to simulate
âNational Research Council, Controlling the Quantum World: The Science of Atoms, Molecules, and
Photons, Washington, D.C.: The National Academies Press, 2007.

48 C o n d e n s e d - M at t e r and M at e r i a l s P h ys i c s
models of some of the most significant outstanding problems in condensed-matter
physics, including high-temperature superconductivity and related strong correla-
tion phenomena. These optical lattice-based systems, acting as âanalog quantum
computers,â may provide solutions to problems that have been found to be essen-
tially unsolvable using conventional digital computers. Most importantly, ultracold
atoms offer the prospect of discovery of wholly new and highly exotic states of
condensed matter that have no roots in traditional material systems.
Emergence in Classical Condensed-Matter SYSTEMS
A number of examples of emergence in classical condensed-matter systems
illustrate the scope and unity of the concepts underlying the study of emergence,
where neither quantum mechanics nor even conventional thermal physics plays any
direct role in determining the emergent behavior (see Figure 2.6). A few examples
are described below.
Granular matter, like other forms of condensed matter, is made up of an enor-
mously large number of simple constituentsâthe individual grains, for instance,
of sand or wheat. The difference is, however, that the grains themselves are very
large compared with the atoms and small molecules that make them up. Since the
FIGURE 2.6â A wide variety of regular patterns spontaneously emerge in many systems driven away
from equilibrium. There is a growing understanding of the variety and complexity of the patterns in
terms of the nonlinear interaction and competition between spatial modes that become unstable ow-
ing to the drive away from equilibrium. The three panels in this figure show results of simulations of
a simple partial differential equation that captures these effectsâthe different patterns are given by
changing parameters. Patterns remarkably similar to these are seen in experimental systems such as
boiling water, vertically shaken fluids, and granular flows. SOURCE: Ron Lifshitz, Tel Aviv University.
Based on R. Lifshitz and D.M. Petrich, âTheoretical Model for Faraday Waves with Multiple-Frequency
Forcing,â Phys. Rev. Lett. 79, 1261-1264 (1997).

How Do Complex Phenomena Emerge from Simple Ingredients? 49
characteristic energy scale that characterizes the quantum motion of a collection
of particles decreases rapidly with the increasing size of the particle, even at the
lowest accessible temperatures quantum effects in granular systems are negligible.
Conversely, even at room temperature or above, thermal effects are also negligible:
the interaction energy between pairs of grains increases with size (roughly in pro-
portion to the surface area) and so is always large compared with the temperature.
Put another way, the ratio of the entropic and interaction contributions to the free
energy at any fixed temperature decreases rapidly with the size of the grains. Thus,
granular matter effectively presents scientists with a problem in which temperature
can also be ignored, so the collective phenomena typically involve nonequilibrium
physics, as discussed in Chapter 5. Nevertheless, emergent phenomena occur in
granular matter in much the same manner that they occur in conventional fluids
and solids, although often with new and fascinating wrinkles.
When a granular material is fluidized, by shaking it vigorously or by blowing
gas through it, the resulting non-equilibrium state has many features in common
with a simple gasâfor example, the individual grains exhibit a distribution of
speeds that is very similar to that of molecules in a gas at an âeffective temperature,â
which depends on how violently the granular matter is shaken. A dense granular
material, like sand on a beach, shares many properties with a solid, including its
ability to support a person. However, unlike a simple solid, where the strain is fairly
smoothly distributed throughout the material, in a compressed granular system the
strains can be highly irregularly distributed along lines of force (Figure 2.7). The
principles that govern the distribution of strain in dense granular matter, and which
features are universal (i.e., do not depend on the nature [size, shape, hardness] of
the individual grains), are at present an area of active research. It is similarly not
fully understood to what extent the motion of broader classes of driven granular
systems can be related to properties of a related equilibrium system at an effective
temperature.
Jamming is a phenomenon in granular materials that, when better understood,
may shed light on a broad class of phenomena in condensed-matter systems. At
low density, it is clearly easy for granular matter to flowâeach grain simply moves
in the general direction of the flow and is occasionally scattered when it collides
with another grain. This is a classical analogue of the motion of quasi-particles in
a Fermi liquid. However, when hard grains, such as grains of sand, reach a critical
density, there is simply no room for the grains to flow. Every grain is jammed in
a cage of other grains from which it cannot escape. Here, the strong correlations
between grains entirely quench the free motion of the individual grains. Since
there is no balance of quantum and classical energies, no competing tendencies of
energy and entropy, this jamming transition may be, in some sense, the simplest
model problem in the physics of strong correlations. Jamming is, in a sense, a purely
geometric phenomenon.

50 C o n d e n s e d - M at t e r and M at e r i a l s P h ys i c s
FIGURE 2.7â A collapsing grain silo provides a dramatic example of the unexpected behavior of granu-
lar materials. If the grains are flowing in some regions and jammed in others within the silo, there can
be large variations of the stress on the silo walls, leading to disaster. SOURCE: J.M.Rotter, University
of Edinburgh, and J.W. Carson, Jenike and Johanson, Inc.

How Do Complex Phenomena Emerge from Simple Ingredients? 51
Realizing the Full Potential of Emergence
Emergent phenomena in condensed matter are often discovered serendipi-
tously. The discovery of superconductivity by Kamerlingh Onnes in 1911 was
certainly accidental. The discovery of the fractional quantum Hall effect by Tsui,
Stormer, and Gossard in 1982 was similarly unanticipated. These two great discov-
eries, decades apart in time, have some important similarities that offer insights into
how to increase the odds for the discovery of emergent phenomena. For example,
both experiments were part of a program of curiosity-driven, âblue-skyâ research,
and both fundamentally altered the landscape of CMMP. At the same time, both
discoveries are intimately connected to the technological side of CMMP. With su-
perconductivity, that connection lay in the future applications of the phenomenon
itself. Conversely, the discovery of the fractional quantum Hall effect was enabled
by technical advances in semiconductor crystal growth critical to the development
of high-speed transistors for telecommunications. These two discoveries beauti-
fully illustrate the inseparability of the applied and fundamental sides of CMMP.
They also illustrate the need to maintain a robust funding base for the pursuit of
curiosity-driven CMMP research and the ready availability of the exotic materials
that enable such great discoveries. Both of these issues figure prominently in the
recommendations of this report.
Superconductivity and the fractional quantum Hall effect were discovered
by investigating the properties of matter under extreme conditions. Kamerlingh
Onnes, having recently succeeded in liquefying helium, was studying the resistivity
of metals cooled to near absolute zero. Tsui, Stormer, and Gossard, also examining
electrical conduction, were subjecting their ultrapure semiconductor samples to the
highest-available magnetic fields. The fruitfulness of high magnetic fields and low
temperatures of course remains fully appreciated, with the National High Magnetic
Field Laboratory in Tallahassee, Florida, the most visible evidence. Beyond high
magnetic fields and low temperatures, CMMP researchers regularly subject their
samples to high pressures, intense electromagnetic fields, dimensional confine-
ment, and other extreme conditions in search of understanding and, best of all,
surprises.
Discoveries of emergent phenomena sometimes have the appearance of mere
lucky breaks in an otherwise random walk. This is no truer of superconductivity or
the fractional quantum Hall effect than it is of Edisonâs discovery of the correct fila-
ment material for incandescent light bulbs. Kamerlingh Onnes was naturally trying
to understand the conduction of electricity in metals in the context of the Drude
theory advanced just a few years before. Similarly, Tsui, Stormer, and Gossard were
guided in part by theoretical predictions that electron gases would freeze directly
into a crystalline solid at high enough magnetic field. Both examples illustrate the

52 C o n d e n s e d - M at t e r and M at e r i a l s P h ys i c s
close interaction between theory and experiment that characterizes CMMP; each
informs and guides the other.
Conclusions
Emergent phenomena in condensed-matter and materials physics are those
that cannot be understood with models that treat the motions of the individual
particles within the material independently. Instead, the essence of emergent phe-
nomena lies in the complex interactions between many particles that result in
the diverse behavior and often unpredictable collective motion of many particles.
It is wonderful and exciting that the well of such phenomena is infinitely deep;
CMMP researchers will never run short of mysteries to solve and phenomena to
exploitâthey are out there for the inquisitive to find.
Emergent phenomena beautifully illustrate the inseparability of the fundamen-
tal and applied research in CMMP. In some cases, the application of an emergent
phenomenon is nearly immediate; in other cases it takes decades to occur; and in
still others it may never occur. At the same time, technical advances in one area of
CMMP can enable the discovery of an exotic phenomenon in a seemingly remote
area of the field.
The nationâs CMMP community has historically been extraordinarily success-
ful at discovering, understanding, and applying emergent phenomena. In terms
of opportunity, the future is extremely bright. Ever-more-complex materials are
being synthesized and ever-more-sophisticated tools are being developed for their
study. The explosion of research on nanoscale systems and the rapidly dissolving
boundaries between CMMP and other scientific disciplines will surely lead to new
vistas in emergent phenomena. The challenge is to make sure that U.S. research-
ers have access to the best new materials and tools and the time and resources to
make the most of them.
The paths between discovery, understanding, and applications of scientific
research are obscure and unpredictable. They are full of sharp turns, dead ends,
and unexpected forks in the road. But they also can lead to beautiful places that
no one knew existed. Robert Frost had it right: It is important to take the road less
traveled, for that will make all the difference.

The development of transistors, the integrated circuit, liquid-crystal displays, and even DVD players can be traced back to fundamental research pioneered in the field of condensed-matter and materials physics (CMPP). The United States has been a leader in the field, but that status is now in jeopardy. Condensed-Matter and Materials Physics, part of the Physics 2010 decadal survey project, assesses the present state of the field in the United States, examines possible directions for the 21st century, offers a set of scientific challenges for American researchers to tackle, and makes recommendations for effective spending of federal funds. This book maintains that the field of CMPP is certain to be principle to both scientific and economic advances over the next decade and the lack of an achievable plan would leave the United States behind. This book's discussion of the intellectual and technological challenges of the coming decade centers around six grand challenges concerning energy demand, the physics of life, information technology, nanotechnology, complex phenomena, and behavior far from equilibrium. Policy makers, university administrators, industry research and development executives dependent upon developments in CMPP, and scientists working in the field will find this book of interest.

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